Question

A triangle has sides A, B, and C. Sides A and B are of lengths `6` and `2`, respectively, and the angle between A and B is `(2pi)/3`. What is the length of side C?

Answer 1

≈ 7.211 units

Explanation:

Given a triangle , where 2 sides and the angle between them are known, we can use the`color(blue)" cosine rule " " to find C "`

`c^2 = a^2 + b^2 - (2ab costheta)`

where a and b are the 2 known sides and `theta" the angle between them "`

here a = 6 , b = 2 and `theta = (2pi)/3`

substitute these values into the equation

`rArr c^2 = 6^2 + 2^2 - [2xx6xx2xxcos((2pi)/3) ]`

= 36 + 4 - (-12) = 52

now `c^2 = 52 rArr c = sqrt52 ≈ 7.211`